List of top Mathematics Questions asked in KCET

If $\frac {(x+1)^2}{x^3+x}=\frac {A}{x}+\frac {Bx+C}{x^2+1}$, then $\sin^{-1} \,A + \tan ^{-1} \,B + sec ^{-1} \,C$ is equal to

If the value of $C_0 + 2 \cdot C_1 + 3 \cdot C_2 + \dots+ (n+1) \cdot C_n=576$ ,then n is equal to

The minimum area of the triangle formed by the variable line $3 \, \cos\,\theta \cdot x + 4 \,\sin \,\theta \cdot y = 12$ and the co-ordinate axes is

The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is

Solution of $e^\frac {dy}{dx} = x$ when $x = 1$ and $y = 0$ is

If one of the slopes of the pair of lines $ax^2 + 2hxy + by^2 = 0$ is $n$ times the other then

The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is

The last digit of number $7^{886}$ is

$p \rightarrow \sim q$ can also be written as

The length of the sub-tangent, ordinate and the sub-normal are in

$\frac {\sin 70^\circ\, +\cos 40^\circ} {\cos 70^\circ + \sin 40^\circ}$=

The least and the greatest distances of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ are

If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is

The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are

The number of solutions of the equation $z^2+\bar{z}=0$, where $z \in C$ are

The characteristic equation of a matrix $A$ is $\lambda^3 - 5\lambda^2 - 3\lambda + 2 = 0$ then $| adj (A) |$ is equal to

The maximum value of $xe^{ -x}$ is

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0,\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0 $ and $ \alpha + \beta + \gamma = \pi, $ then $ \sin 3\alpha + 8 \sin 3\beta + 27 \sin 3\gamma$ =

If $a , b$ and $c$ are three non-coplanar vectors and $p , q$ and $r$ are vectors defined by $p =\frac{ b \times c }{[ a b c ]}, q =\frac{ c \times a }{[ a b c ]}$ and $r =\frac{ a \times b }{[ a b c ]}$, then the value of $( a + b ) \cdot p +( b + c ) \cdot q +( c + a ) \cdot r$ is equal to

If $\alpha $ and $\beta$ are different complex numbers with $ | \beta | = 1$, then $\frac {\beta-\alpha}{1-\overline {\alpha} \beta}$ is equal to

If $ \log_2 (9 ^{x-1} + 7) - \log_2 (3^{x-1 } + 1) = 2 $ then $x$ values are

$2 \cos^{-1} x = \sin^{-1} ({2x \sqrt {1-x^2)}}$ is valid for all values of $x$ satisfying

If $\frac {3x+1}{(x-1)(x+3)} =\frac {A}{x-1} + \frac {B} {x+3} \sin^{-1} \frac {A}{B}$ = is equal to

Length of the subtangent at $ (x_1, y_1)$ on $x^n y^m = a^{m+n}, m, n > 0,$ is